Applied computational geometry in fundamentals of bio-imaging and analysis

作为一名在生物系统工程领域工作的计算机科学家，我的长期研究计划侧重于计算几何在成像和分析食品和生物材料的基础物理科学中的应用。在材料分析中，传统的光谱技术提供化学样品的光谱特征，现代光谱成像提供样品每个像素的整个光谱。虽然每种技术和制造商都有不同空间分辨率的设备，但许多设备每个样本提供数十万像素。同样，光谱分辨率也从多光谱（每像素几十个光谱）到高光谱（每像素几百到几万个光谱）不等。计算几何通常在数据集的几何抽象中分析结构。作为几何结构的一个例子，通过将光谱中的单个峰及其大小视为该数据点的单独数学值（特征），可以将特定物质的光谱视为几何数据。可以分析一系列物质（即数据点），以找到具有相似化学键的化学物质的簇/结构（例如化学亚基团）。拟议研究的长期目标是将计算几何建立为光谱信号分析和获取的关键组成部分，并将其用于确定食品和生物材料的质量。我的短期目标集中在两个方面：使用最近邻方法对光谱数据进行聚类和分类分析，并使用多边形简化和估计技术来改进核磁共振波谱学中的数据采集。

As a computer scientist working in the discipline of biosystems engineering, my long term research program focuses on the application of computational geometry to the fundamental physical sciences of imaging and analyzing food and biological materials.  In the analysis of materials, traditional spectroscopic techniques provide the spectral signature of a chemical sample, modern spectroscopic imaging provides entire spectra at each pixel of a sample.  While each technology and manufacturer has equipment with differing spatial resolutions many devices offer hundreds of thousand of pixels per sample.  Similarly spectral resolution varies from the multispectral (tens of spectra per pixel) to hyperspectral (hundreds to tens of thousands per pixel).Computational geometry typically analyzes structure within a geometric abstraction of a data set.  As an example of geometric structure, a particular substance's spectra can be considered geometric data by considering individual peaks in the spectra and their magnitude as separate mathematical values (features) of that data point.  Sets of substances (i.e., data points) can be analyzed to find clusters/structures of chemicals with similar chemical bonds (e.g. chemical sub-groups).   The long term goal of the proposed research is to establish computational geometry as a key component in the analysis and acquisition of spectral signals and their use in the determination of quality of food and biological materials.  My short term goals focus on two areas:  the use of nearest neighbour methods to perform cluster and classification analysis of spectral data and the use of polygonal simplification and estimation techniques to improve data acquisition in nuclear magnetic resonance spectroscopy.